'''1.Determination of initiation age (a<sub>i</sub>) and C+D''':[[Image:Theoretical_age_distr.jpg|left|200px]]

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===Determination of initiation age (a<sub>i</sub>) and C+D:===

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[[Image:Theoretical_age_distr.jpg|left|200px]]

From flow cytometry analysis of cells treated with rifampicin and cephalexin (run-out histogram) the proportions of cells that had not initiated replication at the time of drug action (4-origin-cells, streaked) and cells that had initiated (8-origin-cells) can be estimated.The initiation age (a<sub>i</sub>) can be found from the theoretical age distribution described by this formula,

From flow cytometry analysis of cells treated with rifampicin and cephalexin (run-out histogram) the proportions of cells that had not initiated replication at the time of drug action (4-origin-cells, streaked) and cells that had initiated (8-origin-cells) can be estimated.The initiation age (a<sub>i</sub>) can be found from the theoretical age distribution described by this formula,

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'''F = 2 - 2<sup>((τ-a<sub>i</sub>)/τ)</sup>'''

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'''<math>F=2-2^{\frac{(\tau-a_i)}{\tau}}</math>'''

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where F is the fraction of cells that had not initiated and τ is the generation time, or from the estimated graph of the theoretical age distribution (streaked portion).

where F is the fraction of cells that had not initiated and τ is the generation time, or from the estimated graph of the theoretical age distribution (streaked portion).

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This gives:

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'''<math>a_i=\tau-\frac{log(2-F)}{log2}*\tau</math>'''

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which is the same as this (log2 is 1):

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'''<math>a_i=\tau-log(2-F)*\tau</math>'''

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If you have for example a generation time τ=84 minutes and the portion of cells with 4 origins is 66% the formula gives:

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'''<math>a_i=84-log(2-0.66)*84=48.5</math>'''

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[[Image:C+D_1.jpg|left|250px]]

[[Image:C+D_1.jpg|left|250px]]

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===Determination of the C and D periods:===

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The C period is found from the ''oriC/terC'' ratio obtained by Southern blot or qPCR analysis ([[oriC/ter ratio determination]]) and the generation time (τ):

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'''<math>\frac{oriC}{terC}=2^{\frac{C}{\tau}}</math>'''

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which gives:

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'''<math>C=log(\frac{oriC}{terC})*{\tau}</math>'''

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The D period is found from the C+D and C period:

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'''<math>D = (C+D) - C</math>'''

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Example (continues):

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C period calculated from the ''oriC/terC'' ratio: 49 min

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D period = (C+D) – C

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D period = 76 min – 49 min = 27 min

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'''2. Determination of the C and D periods:'''

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[[Image:C+D_2.jpg|left|250px]]

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The C period is found from the ''oriC/terC'' ratio obtained by Southern blot analysis and the generation time (τ):

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===The theoretical exponential DNA histogram:===

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'''''oriC/terC''=2<sup>C/τ</sup>'''

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A theoretical exponential DNA histogram can be drawn to check whether the obtained values fit with the experimental data. From the C+D period the DNA content of the cells at different time points in the cell cycle can be calculated.

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Example:

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The D period is found from the C+D and C period:

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[[Image:Theoretical_exp_histogram.jpg|left|400px]]

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'''D = (C+D) - C'''

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[[Image:Theoretical_exp_histogram2.jpg|left|200px]]

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The individual values of C and D can be varied

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to obtain a shape of the theoretical histogram

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that gives the best fit to the experimental histogram.

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===Calculation of the average number of replication forks when D=τ:===

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In the example given above, 23% of the cells contain 4 replication forks (4-origin peak in run-out histogram) and 77% contain 12 replication forks (8-origin peak), hence the average number of replication forks in the cell population will be:

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(4 x 0.23) + (12 x 0.77) = 10.2 forks

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===Calculation of the average number of replication forks when D≠τ:===

Determination of initiation age (ai) and C+D:

From flow cytometry analysis of cells treated with rifampicin and cephalexin (run-out histogram) the proportions of cells that had not initiated replication at the time of drug action (4-origin-cells, streaked) and cells that had initiated (8-origin-cells) can be estimated.The initiation age (ai) can be found from the theoretical age distribution described by this formula,

where F is the fraction of cells that had not initiated and τ is the generation time, or from the estimated graph of the theoretical age distribution (streaked portion).

This gives:

which is the same as this (log2 is 1):

ai = τ − log(2 − F) * τ

If you have for example a generation time τ=84 minutes and the portion of cells with 4 origins is 66% the formula gives:

ai = 84 − log(2 − 0.66) * 84 = 48.5

The C+D period is estimated from the initiation age (ai), the generation time (τ) and the number of generations spanned per cell cycle.

Example:

4-origin-cells: 23 %

Generation time (τ): 27 min

Initiation age (ai): 5 min

Determination of the C and D periods:

The C period is found from the oriC/terC ratio obtained by Southern blot or qPCR analysis (oriC/ter ratio determination) and the generation time (τ):

which gives:

The D period is found from the C+D and C period:

D = (C + D) − C

Example (continues):

C period calculated from the oriC/terC ratio: 49 min

D period = (C+D) – C

D period = 76 min – 49 min = 27 min

The theoretical exponential DNA histogram:

A theoretical exponential DNA histogram can be drawn to check whether the obtained values fit with the experimental data. From the C+D period the DNA content of the cells at different time points in the cell cycle can be calculated.

Example:

The individual values of C and D can be varied

to obtain a shape of the theoretical histogram

that gives the best fit to the experimental histogram.

Calculation of the average number of replication forks when D=τ:

In the example given above, 23% of the cells contain 4 replication forks (4-origin peak in run-out histogram) and 77% contain 12 replication forks (8-origin peak), hence the average number of replication forks in the cell population will be: